Polish cavalry takes it origin from whoever got bright idea to mount the horse, take a weapon (a spear, a mullet or a sword) and fight enemy using hight advantage and better horse mobility than human. More seriously it can trace its roots to mounted knights. When knights bacame obsolete soldiers mounted on horses did not.
In XV century cavalry available to Polish King Wladislaw II Jagiello (he was Lithuanian, Poland was Kingdom of Two Nations formed from union between Kingdom of Poland and The Great Duchess of Lithuania (?)) for the Tannenberg battle in 1410 with Teutonic Knights (Jagiello camp was in village Grunwald so for Poles it was Grunwald battle) showed how many nationalities were ruled by him. There was Polish cavalry (mostly knights - not as well armored as opponents) it could be considered heavy cavalry, there was Lithuanian cavalry and Russian or maybe Belorussian and Tartars (do they have something in common with Mongols ). All these could be considered light cavalry.
200 years later during Swedish invasion (Potop Szwedzki) the most famous was Polish heavy cavalry called husaria (hussars). They were used to break throught the enemy line and open path for lighter soldiers to explore the break in. Just like the tanks are used for almost 100 years. No wonder that hussar's wings (the rider was quite heavily armoured and part of the suite were up-side down J shaped two attachments on the back with feathers attached; one story claims that they made it harder for the rider to be dismounted with a lasso but another one is that a few hundred men on heavy horses coming at enemy fast made additional noise; so it was a part of psychological war) were made an emblem of Polish tankers.
One of the most famous displays of heavy cavalry was the Battle of Kircholm in 1605. Polish/Lithuanian forces commanded by Jan Karol (John Charles) Chodkiewicz numbered less than 4000 people (2700 cavalry, 1000 infantry) beat Swedish king Charles IX with 11000 people (2500 cavalry, 8200 infantry).
Before the WW2 Poland had 11 cavalry brigades and 2 armoured-mechanized brigades. XX century cavalry, unlike the old ones, was not meant to fight mounted. Machine gun discouraged such a way of fighting.
In 1920 a war between the USSR and Poland featured the last great cavallery battle in Europe. Twe battle at the river Wisla (Vistula) was won by the Polish side despite the fact they were outnumbered by the opponent. The battle is consiedred as one of the most significant in the world's history as it endeded the communist plans of Europe expansion.
The weaknesses of cavalry unit were: - damaged machinery can be fixed relatively fast, it is longer process with a horse; one cannot revive a horse; - some soldiers, instead of fighting, must have taken care of horses during the battle. If I am not mistaken it was 20-25% of the fighting force. Such position was called "koniowodny".
Strong points: - Poland did not have enough infrastructure to support gasoline distribution. One of the forseen enemies was Soviet Union and cavalry with its independence from gasoline was an asset not burden. Wehrmacht used cavalry on eastern front so it was not that bad idea. - Many conscripts had more experience with horses than cars. Less training.
